# Passive Flow Control for Drag Reduction on a Cylinder in Cross-Flow Using Leeward Partial Porous Coatings

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic showing the porous coating on the leeward side of a cylinder and the definition of circumferential angle $\theta $ and porous coating angle $\beta $.

**Figure 2.**(

**a**) Drag coefficient and (

**b**) lift coefficient as a function of flow time during the initial transition period before statistically quasi-steady-state conditions are reached. The data shown represent a smooth cylinder at $Re=4.2\times {10}^{4}$.

**Figure 3.**(

**a**) A structured mesh developed for the solid cylinder case with 155,000 mesh elements. (

**b**) Mesh for a 160${}^{\circ}$ porous coating.

**Figure 4.**Time-averaged ${C}_{p}$ for the smooth cylinder and varying coating angle $\beta $ at $Re$ = $4.2\times {10}^{4}$, constant thickness $t/D$ = 14.3% and a porosity of 20 PPI. (

**a**) $\beta ={100}^{\circ}$. (

**b**) $\beta ={160}^{\circ}$.

**Figure 5.**Time-averaged ${C}_{p}$ for the smooth cylinder and varying coating angle $\beta $ with standard deviation bars at $Re$ = $4.2\times {10}^{4}$, constant thickness $t/D$ = 14.3% and a porosity of 20 PPI. (

**a**) $\beta ={100}^{\circ}$. (

**b**) $\beta ={160}^{\circ}$.

**Figure 6.**Percentage change in the time-averaged drag coefficient with porous coating angle $\beta $ compared to the experimental results adapted from Klausmann and Ruck [25]. Constant porosity of 20 PPI and coating thickness $t/D$ = 14.3%.

**Figure 7.**Variation in the separation angle with the time-averaged drag coefficient at $Re$ = $4.2\times {10}^{4}$, constant thickness $t/D$ = 14.3% and a porosity of 20 PPI.

**Figure 8.**Circumferential average of the RMS radial velocity across the porous zone outer boundary for varying coating angle $\beta $ at $Re$ = $4.2\times {10}^{4}$, constant thickness $t/D$ = 14.3% and a porosity of 20 PPI.

**Figure 9.**Variation in average turbulence intensity at the outlet with the time-averaged drag coefficient at $Re$ = $4.2\times {10}^{4}$, thickness $t/D$ = 14.3% and a porosity of 20 PPI.

**Figure 10.**Instantaneous contours of velocity at $Re=4.2\times {10}^{4}$. (

**a**) Smooth cylinder (diameter D). (

**b**) Fully coated cylinder (thickness $t/D$ = 14.3% and a porosity of 20 PPI). The black circle indicates the outer diameter D of the porous coating.

**Figure 11.**Contours of velocity at $Re=4.2\times {10}^{4}$. (

**a**) Smooth cylinder. (

**b**) $\beta ={70}^{\circ}$ (thickness $t/D$ = 14.3% and a porosity of 20 PPI). (

**c**) $\beta ={160}^{\circ}$ (thickness $t/D$ = 14.3% and a porosity of 20 PPI).

**Figure 12.**Flow recirculation in the $\beta ={160}^{\circ}$ coating at $Re=4.2\times {10}^{4}$, thickness $t/D$ = 14.3% and a porosity of 20 PPI. (

**a**) Velocity streamlines. (

**b**) Pressure contours.

**Table 1.**Effect of mesh density on the characteristic dimensionless numbers averaged between 1 and 2 s of flow time in quasi-steady-state flow at $Re$ = $4.2\times {10}^{4}$, compared to the values from the experimental and numerical literature.

Case | ${\mathit{C}}_{\mathit{d}}$ | ${\mathit{C}}_{\mathit{l}}^{\prime}$ | $\mathit{St}$ |
---|---|---|---|

Present study (77,000 elements) | 1.014 | 0.752 | 0.25 |

Present study (109,000 elements) | 1.023 | 0.767 | 0.25 |

Present study (155,000 elements) | 1.065 | 0.846 | 0.25 |

Present study (220,000 elements) | 1.034 | 0.782 | 0.25 |

Experimental [25] | 1.24 | - | - |

Experimental [32,33,34,35] | 1.2 | 0.45–0.53 | 0.18 |

2D $k-\omega $ SST ($Re$ = $9\times {10}^{4}$) [37] | 0.944 | 0.762 | 0.247 |

2D $k-\omega $ SST ($Re$ = $9.3\times {10}^{4}$) [18] | 1.31 | 0.88 | 0.196 |

3D LES ($Re$ = $9\times {10}^{4}$) [37] | 1.08 | 0.485 | 0.191 |

**Table 2.**Comparison of the results for the varying partial porous coating angles, the fully coated cylinder ($\beta ={360}^{\circ}$) and the smooth cylinder ($\beta ={0}^{\circ}$).

$\mathit{\beta}$ | ${\mathit{C}}_{\mathit{d}}$ | $\mathbf{\Delta}\%$ | ${\mathit{C}}_{\mathit{l}}^{\prime}$ | $\mathbf{\Delta}\%$ | $\mathit{St}$ | $\mathbf{\Delta}\%$ | ${\mathit{\theta}}_{\mathit{sep}}$ | $\mathbf{\Delta}\%$ |
---|---|---|---|---|---|---|---|---|

0${}^{\circ}$ | 1.065 | - | 0.846 | - | 0.25 | - | 90.69${}^{\circ}$ | - |

40${}^{\circ}$ | 0.945 | −11.3 | 0.523 | −38.2 | 0.25 | 0.0 | 87.26${}^{\circ}$ | −3.8 |

70${}^{\circ}$ | 0.900 | −15.5 | 0.389 | −54.1 | 0.25 | 0.0 | 86.34${}^{\circ}$ | −4.8 |

100${}^{\circ}$ | 0.912 | −14.3 | 0.396 | −53.1 | 0.26 | 4.0 | 86.89${}^{\circ}$ | −4.2 |

130${}^{\circ}$ | 1.008 | −5.4 | 0.589 | −30.4 | 0.26 | 4.0 | 89.07${}^{\circ}$ | −1.8 |

160${}^{\circ}$ | 1.528 | 43.4 | 1.187 | 40.3 | 0.27 | 8.0 | 93.60${}^{\circ}$ | 3.2 |

360${}^{\circ}$ | 1.511 | 41.8 | 0.322 | −61.9 | 0.24 | −4.0 | 139.83${}^{\circ}$ | 54.2 |

**Table 3.**Comparison of the normalised wake widths $w/D$ for the varying porous coating angles and the smooth cylinder ($\beta ={0}^{\circ}$).

$\mathit{\beta}$ | $\mathit{w}/\mathit{D}$ | $\mathbf{\Delta}\%$ |
---|---|---|

0${}^{\circ}$ | 2.88 | - |

40${}^{\circ}$ | 2.83 | −1.7 |

70${}^{\circ}$ | 2.83 | −1.7 |

100${}^{\circ}$ | 2.78 | −3.4 |

130${}^{\circ}$ | 2.83 | −1.7 |

160${}^{\circ}$ | 3.32 | 15.5 |

360${}^{\circ}$ | 3.67 | 27.6 |

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**MDPI and ACS Style**

Guinness, I.; Persoons, T. Passive Flow Control for Drag Reduction on a Cylinder in Cross-Flow Using Leeward Partial Porous Coatings. *Fluids* **2021**, *6*, 289.
https://doi.org/10.3390/fluids6080289

**AMA Style**

Guinness I, Persoons T. Passive Flow Control for Drag Reduction on a Cylinder in Cross-Flow Using Leeward Partial Porous Coatings. *Fluids*. 2021; 6(8):289.
https://doi.org/10.3390/fluids6080289

**Chicago/Turabian Style**

Guinness, Imogen, and Tim Persoons. 2021. "Passive Flow Control for Drag Reduction on a Cylinder in Cross-Flow Using Leeward Partial Porous Coatings" *Fluids* 6, no. 8: 289.
https://doi.org/10.3390/fluids6080289